Factorization of the dijet cross section with the Georgi jet algorithm in $e^+ e^-$ annihilation

TL;DR

This paper analyzes the dijet cross section in electron-positron annihilation using the Georgi jet algorithm, demonstrating factorization, infrared finiteness, and resummation of large logarithms, and establishing its equivalence to other jet algorithms.

Contribution

It provides a next-to-leading order calculation and resummation for the Georgi jet algorithm, showing its equivalence to established algorithms in $e^+ e^-$ collisions.

Findings

Factorization into hard, collinear, and soft functions achieved.

Next-to-leading order functions are infrared finite.

Large logarithms are resummed at next-to-leading logarithmic accuracy.

Abstract

We consider the dijet cross section in $e^+ e^-$ annihilation using the Georgi jet algorithm, or the maximizing jet algorithm. The cross section is factorized into the hard, collinear and soft parts. Each factorized function is computed to next-to-leading order, and is shown to be infrared finite. The large logarithms are resummed at next-to-leading logarithmic accuracy. By analyzing the phase space for the jet algorithm, the Georgi algorithm turns out to be equivalent to the Sterman-Weinberg and the cone-type algorithms.